Tuned intrinsic kT parameters ShowerHandler:IntrinsicPtGaussian in Herwig with the underlying-event tune CH2 at nucleon-nucleon center-of-mass energy from 38.8 GeV to 13 TeV.

Tuned intrinsic kT parameters ShowerHandler:IntrinsicPtGaussian in Herwig with the underlying-event tune CH3 at nucleon-nucleon center-of-mass energy from 38.8 GeV to 13 TeV.

Tuned intrinsic kT parameters BeamRemnants:PrimordialkThard in Pythia with the underlying-event tune CP5 and ISR starting scale SpaceShower:pT0Ref = 1 GeV at nucleon-nucleon center-of-mass energy from 38.8 GeV to 13 TeV.

Tuned intrinsic kT parameters ShowerHandler:IntrinsicPtGaussian in Herwig with the underlying-event tune CH3 and ISR starting scale SudakovCommon:pTmin=0.7 GeV at nucleon-nucleon center-of-mass energy from 38.8 GeV to 13 TeV.

Tuned intrinsic kT parameters BeamRemnants:PrimordialkThard in Pythia with the underlying-event tune CP5 at proton-proton center-of-mass energy 38.8 GeV versus the dilepton mass range of the process.

Tuned intrinsic kT parameters BeamRemnants:PrimordialkThard in Pythia with the underlying-event tune CP5 at proton-proton center-of-mass energy 8000 GeV versus the dilepton mass range of the process.

Tuned intrinsic kT parameters BeamRemnants:PrimordialkThard in Pythia with the underlying-event tune CP5 at proton-nucleon center-of-mass energy 8160 GeV versus the dilepton mass range of the process.

Tuned intrinsic kT parameters BeamRemnants:PrimordialkThard in Pythia with the underlying-event tune CP5 at proton-nucleon center-of-mass energy 13000 GeV versus the dilepton mass range of the process.

Tuned intrinsic kT parameters ShowerHandler:IntrinsicPtGaussian in Herwig with the underlying-event tune CH2 at proton-proton center-of-mass energy 38.8 GeV versus the dilepton mass range of the process.

Tuned intrinsic kT parameters ShowerHandler:IntrinsicPtGaussian in Herwig with the underlying-event tune CH2 at proton-proton center-of-mass energy 8000 GeV versus the dilepton mass range of the process.

Tuned intrinsic kT parameters ShowerHandler:IntrinsicPtGaussian in Herwig with the underlying-event tune CH2 at proton-nucleon center-of-mass energy 8160 GeV versus the dilepton mass range of the process.

Tuned intrinsic kT parameters ShowerHandler:IntrinsicPtGaussian in Herwig with the underlying-event tune CH2 at proton-proton center-of-mass energy 13000 GeV versus the dilepton mass range of the process.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-proton center-of-mass energy 38.8 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-proton center-of-mass energy 62 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-proton center-of-mass energy 200 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-anti-proton center-of-mass energy 1800 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-anti-proton center-of-mass energy 1960 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-proton center-of-mass energy 2760 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-proton center-of-mass energy 8000 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-nucleon center-of-mass energy 8160 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-proton center-of-mass energy 13000 GeV when fitting to the CMS measurement.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters among various generator settings at proton-proton center-of-mass energy 13000 GeV when fitting to the LHCb measurement.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-proton center-of-mass energy 38.8 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-proton center-of-mass energy 62 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-proton center-of-mass energy 200 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-anti-proton center-of-mass energy 1800 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-anti-proton center-of-mass energy 1960 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-proton center-of-mass energy 2760 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-proton center-of-mass energy 8000 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-nucleon center-of-mass energy 8160 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-proton center-of-mass energy 13000 GeV when fitting to the CMS measurement.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Pythia at proton-proton center-of-mass energy 13000 GeV when fitting to the LHCb measurement.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-proton center-of-mass energy 38.8 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-proton center-of-mass energy 62 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-proton center-of-mass energy 200 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-anti-proton center-of-mass energy 1800 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-anti-proton center-of-mass energy 1960 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-proton center-of-mass energy 2760 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-proton center-of-mass energy 8000 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-nucleon center-of-mass energy 8160 GeV.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-proton center-of-mass energy 13000 GeV when fitting to the CMS measurement.

Covariance of the data uncertainty contribution to the tuned intrinsic kT parameters between the two generator settings of Herwig at proton-proton center-of-mass energy 13000 GeV when fitting to the LHCb measurement.

Self-Normalized $J/\psi$ yields in the same arms before and after dimuon subtraction and the comparison with PYTHIA 8 simulations

Self-normalized $\psi(2S)$ to $J/\psi$ yields ratio as a function of Self-normalized $N_{ch}$ in the same arms

Self-normalized $\psi(2S)$ to $J/\psi$ yields ratio as a function of Self-normalized $N_{ch}$ in opposite arms

Distributions of $m_T$ in the $W^{+}$ signal selection for mu final states for the pp collisions at $\sqrt{s}=$ 13TeV after the maximum likelihood fit. The EW backgrounds include the contributions from DY, $W\to\tau\nu$, and diboson processes.

Distributions of $m_T$ in the $W^{-}$ signal selection for e final states for the pp collisions at $\sqrt{s}=$ 5TeV after the maximum likelihood fit. The EW backgrounds include the contributions from DY, $W\to\tau\nu$, and diboson processes.

Distributions of $m_T$ in the $W^{-}$ signal selection for mu final states for the pp collisions at $\sqrt{s}=$ 5TeV after the maximum likelihood fit. The EW backgrounds include the contributions from DY, $W\to\tau\nu$, and diboson processes.

Distributions of $m_T$ in the $W^{-}$ signal selection for e final states for the pp collisions at $\sqrt{s}=$ 13TeV after the maximum likelihood fit. The EW backgrounds include the contributions from DY, $W\to\tau\nu$, and diboson processes.

Distributions of $m_T$ in the $W^{-}$ signal selection for mu final states for the pp collisions at $\sqrt{s}=$ 13TeV after the maximum likelihood fit. The EW backgrounds include the contributions from DY, $W\to\tau\nu$, and diboson processes.

Distributions of $m_{ll}$ in the Z signal selection for ee final states for the pp collisions at $\sqrt{s}=$ 5TeV after the maximum likelihood fit. The EW backgrounds include the contributions from DY, $W\to l\nu$, and diboson processes.

Distributions of $m_{ll}$ in the Z signal selection for mumu final states for the pp collisions at $\sqrt{s}=$ 5TeV after the maximum likelihood fit. The EW backgrounds include the contributions from DY, $W\to l\nu$, and diboson processes.

Distributions of $m_{ll}$ in the Z signal selection for ee final states for the pp collisions at $\sqrt{s}=$ 13TeV after the maximum likelihood fit. The EW backgrounds include the contributions from DY, $W\to l\nu$, and diboson processes.

Distributions of $m_{ll}$ in the Z signal selection for mumu final states for the pp collisions at $\sqrt{s}=$ 13TeV after the maximum likelihood fit. The EW backgrounds include the contributions from DY, $W\to l\nu$, and diboson processes.

Figure 4 Fiducial cross sections and ratios for $W\to\ell\nu$ and $Z\to\ell\ell$ processes at 13TeV

Figure 5 Fiducial cross sections and ratios for $W\to\ell\nu$ and $Z\to\ell\ell$ processes at 5.02TeV

Figure 6 Fiducial cross sections and ratios for $W\to\ell\nu$ and $Z\to\ell\ell$ processes between 13TeV and 5.02TeV

Figure 7 Total cross sections and ratios for $W\to\ell\nu$ and $Z\to\ell\ell$ processes at 13TeV

Figure 8 Total cross sections and ratios for $W\to\ell\nu$ and $Z\to\ell\ell$ processes at 5.02TeV

Figure 9 Total cross sections and ratios for $W\to\ell\nu$ and $Z\to\ell\ell$ processes between 13TeV and 5.02TeV

Summary of theoretical predictions of the total inclusive cross sections for W and Z boson production times leptonic branching fractions at ppbar collisions.

Summary of experimental measurements of the total inclusive cross sections for W and Z boson production times leptonic branching fractions at UA1 and UA2.

Summary of experimental measurements of the total inclusive cross sections for W and Z boson production times leptonic branching fractions at D0.

Summary of experimental measurements of the total inclusive cross sections for W and Z boson production times leptonic branching fractions at CDF.

Summary of theoretical predictions of the total inclusive cross sections for W boson production times leptonic branching fractions at pp collisions.

Summary of experimental measurements of the total inclusive cross sections for Z boson production times leptonic branching fractions at pp collisions.

Summary of experimental measurements of the total inclusive cross sections for W and Z boson production times leptonic branching fractions at CMS.

Values of $N^{EXP}_{coll}$ versus $p_{T}$ as defined in Eq. 2 for three d+Au event classes, (a) $0\%–100\%$, (b) $0\%–5\%$ and (c) $60\%–88\%$. Also shown are fits to the data (solid lines) and the corresponding value $N^{GL}_{coll}$ (dashed lines).

Panels (d) to (f) show the nuclear modification factors $R^{\pi^{0}}_{dAu,EXP}$, calculated with Eq. 3, for the same event selections as in (a) to (c) together with fits to the data, (d) $0\%–100\%$, (e) $0\%–5\%$ and (f) $60\%–88\%$.

The Ratio $N^{EXP}_{coll}/N^{GL}_{coll}$ as a function of $N^{EXP}_{coll}$. Horizontal and vertical bars are the statistical uncertainties. The values for $0\%–100\%$ d+Au collisions are represented by a solid blue line, with the statistical uncertainty given as band. The scale uncertainties that are common to all data points are shown for the $0\%–100\%$ value.

Average $R^{\pi^{0}}_{dAu,EXP}$ as a function of $N^{EXP}_{coll}$. Horizontal and vertical bars are the statistical uncertainties. The values for $0\%–100\%$ d+Au collisions are represented by a solid blue line, with the statistical uncertainty given as band. The scale uncertainties(16.5%) that are common to all data points are shown for the $0\%–100\%$ value.

Average $R^{\pi^{0}}_{dAu,EXP}$ as a function of $N^{EXP}_{coll}$. Horizontal and vertical bars are the statistical uncertainties. The values for $0\%–100\%$ d+Au collisions are represented by a solid blue line, with the statistical uncertainty given as band. The scale uncertainties($16.5\%$) that are common to all data points are shown for the $0\%–100\%$ value. The systematic uncertainties on $N^{EXP}_{coll}$, $\approx16\%$, are dominated by uncertainties on the p+p data set and thus are a common scale uncertainty for all d+Au event classes.

The $\phi$-meson integrated nuclear modification factors $R_{AB}$ measured as a function of $N_{part}$

The comparison of $\phi$ meson (a) $v_2$ and (b) $v_2/(\epsilon N_{part}^{1/3})$ measured as a function of $p_T$ in Cu+Au collisions at $\sqrt{s}$ = 200 GeV and U+U collisions at $\sqrt{s}$ = 193 GeVat midrapidity (|η| < 0.35)

The comparison of elliptic flow (a) $v_2$ values measured for $\phi$ mesons as a function of $p_T$ in $0\%–20\%$ Cu+Au collisions

The comparison of elliptic flow (b) $v_2$ values measured for $\phi$ mesons as a function of $KE_T$ in $0\%–20\%$ Cu+Au collisions

The comparison of elliptic flow (c) $v_2/n_q$ values measured for $\phi$ mesons as a function of $KE_T/n_q$ in $0\%–20\%$ Cu+Au collisions

The comparison of elliptic flow (a) $v_2$ values measured for $\phi$ mesons as a function of $p_T$ in $20\%–60\%$ Cu+Au collisions

The comparison of elliptic flow (b) $v_2$ values measured for $\phi$ mesons as a function of $KE_T$ in $20\%–60\%$ Cu+Au collisions

The comparison of elliptic flow (c) $v_2/n_q$ values measured for $\phi$ mesons as a function of $KE_T/n_q$ in $20\%–60\%$ Cu+Au collisions

The comparison of elliptic flow (a) $v_2$ values measured for $\phi$ mesons as a function of $p_T$ in $0\%–50\%$ U+U collisions

The comparison of elliptic flow (b) $v_2$ values measured for $\phi$ mesons as a function of $KE_T$ in $0\%–50\%$ U+U collisions

The comparison of elliptic flow (c) $v_2/n_q$ values measured for $\phi$ mesons as a function of $KE_T/n_q$ in $0\%–50\%$ U+U collisions

Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ mesons. \textbf{a)} example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{b)} example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{c)} extracted yields of $\phi$ as a function of $\cos \theta^*$; \textbf{d)} extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ mesons. \textbf{a)} example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{b)} example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{c)} extracted yields of $\phi$ as a function of $\cos \theta^*$; \textbf{d)} extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ mesons. \textbf{a)} example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{b)} example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{c)} extracted yields of $\phi$ as a function of $\cos \theta^*$; \textbf{d)} extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Efficiency corrected $\phi$-meson yields as a function of cos$\theta$* and corresponding fits with Eq.1 in the method section.

Efficiency and acceptance corrected $K^{*0}$-meson yields as a function of cos$\theta$* and corresponding fits with Eq.4 in the method section.

$\phi$-meson $\rho_{00}$ obtained from 1st- and 2nd-order event planes. The red stars (gray squares) show the $\phi$-meson $\rho_{00}$ as a function of beam energy, obtained with the 2nd-order (1st-order) EP.

$\phi$-meson $\rho_{00}$ with respect to different quantization axes. $\phi$-meson $\rho_{00}$ as a function of beam energy, for the out-of-plane direction (stars) and the in-plane direction (diamonds). Curves are fits based on theoretical calculations with a $\phi$-meson field. The corresponding $G_s^{(y)}$ values obtained from the fits are shown in the legend.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

Global spin alignment measurement of $\phi$ and $K^{*0}$ vector mesons in Au+Au collisions at 0-20\% centrality. The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for $K^{*0}$-meson, obtained with the 2nd-order EP.

Global spin alignment measurement of $\phi$ and $K^{*0}$ vector mesons in Au+Au collisions at 0-20\% centrality. The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for $K^{*0}$-meson, obtained with the 2nd-order EP.